MAE 342 – Kinematics and Dynamics of Machinery

Analysis of Mechanism Velocity

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Velocity – Important Equations

• For calculating velocities, there are four important equations:

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Velocity and Point Displacement

• Velocity is related to point displacement through:

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Moving Body (Velocity Difference)

• What if we have two points on a rigid body?

MAE 342 – Kinematics & Dynamics of Machinery

Moving Body (Apparent Velocity) • What if we have two bodies (looking at a point on a

third body)?

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MAE 342 – Kinematics & Dynamics of Machinery

Moving Body(Apparent Angular Velocity) • What if we have two bodies (looking at the rotation

of a third body)?

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What is an “Instant Center”

• The instantaneous center of velocity is:

the instantaneous location of a pair of coincident points of two different rigid bodies for which the absolute velocities of the two points are equal.

• What happens:

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Finding the instant center

• For body with respect to absolute coordinate system

� If velocity of point and angular velocity are known:

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Finding the instant center

� If the velocities of two points are known

Velocities not parallel Velocities are parallel

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Aronhold-Kennedy Theorem

• If there are three bodies, the instant centers between each pair of bodies will lie on the same line.

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Application to automobile design